To determine the phase transition point and to investigate the properties of the phase transition, we need to calculate the order parameter as a continuous function of temperature and quark mass.
The reweighting method is useful for calculating physical quantities as continuous functions by Monte Carlo simulations [1]}.
However, in order to apply the reweighting method to investigate the quark mass dependence, it is necessary to calculate the quark determinant, which requires large computational costs.
Therefore, in Refs. [2]}, [3]}, [4]}, the reweighting method was performed by Taylor-expanding the quark determinant with the hopping parameters and calculating the expansion coefficients.
To investigate the heavy quark region, the Taylor expansion around zero hopping parameter (hopping parameter expansion) is useful.
The reweighting factor can be given by calculating Wilson loops and Polyakov loops, and
the reweighting factor adds the effect of dynamic quarks to the quenched QCD simulations.
